Everyone, thanks for your help I have one further question. My original question was how could two trains collide seeing that there are an infinite amount of points between the two trains. I would think the trains would continue to travel along this string of infinite points never reaching its destination ( the collision). But here is another way to look at it. As the trains came closer and closer towards each other, the amount of space remaining between the trains would shrink. Now if we were to magnify this remaining space, and zoom in at the same rate the space is shrinking, we could maintain a view of this empty space. So... how would this empty space ever disappear, Or how would this empty space ever close and allow the trains to touch?